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Chazal make a big deal out the fact that the ashes of the Parah Adumah are מטהר את הטמא and מטמא את הטהור. It is considered to be the thing that made Parah Adumah inexplicable even to Shlomo Hamelech.
I was wondering why the exact same thing is not said to be happening with the laws of Negaim, tzoraas. One din of tzoraas is מחיה - a place where there is no tzoraas. Paradoxically, that healthy skin is a sign of tumah.
Also, the whole 8th perek is about the din of פורח, where the person becomes completely covered with tzoraas. There is a special gezeiras hakasuv (Vayikra 13:12-13) that this event, which seems to be the worst possible case of tzoraas, is actually tahor. [That itself is an example of a seeming self-contradiction, see Zarka's answer.]
However, the mishnah makes clear that this is only true if the person was already tamei (or at least confined). Here's the first mishnah there, but it's repeated throughout the perek:

הַפּוֹרֵחַ מִן הַטָּמֵא, טָהוֹר. חָזְרוּ בוֹ רָאשֵׁי אֵבָרִים, טָמֵא, עַד שֶׁתִּתְמַעֵט בַּהַרְתּוֹ מִכַּגְּרִיס. מִן הַטָּהוֹר, טָמֵא. חָזְרוּ בוֹ רָאשֵׁי אֵבָרִים, טָמֵא, עַד שֶׁתַּחֲזֹר בַּהַרְתּוֹ לִכְמוֹת שֶׁהָיְתָה:
If a nega broke out completely upon one who was unclean, he becomes clean. If the ends of his limbs reappeared, he becomes unclean until the bright spot is reduced to less than the size of a split bean.
[If it broke out completely upon him] when he was clean, he becomes unclean. If the ends of his limbs reappeared, he remains unclean until his bright spot resumes its former size.

So פורח makes pure the impure, and impure the pure. Do Chazal note this and if not why not?

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Chazal do note this, but they put their observation into the mouth of Korach: see Yerushalmi Sanhedrin, where Korach points out a series of inconsistencies in halachah, including the paradox of whole-body tzara’at.

(Scholars argue that Chazal were troubled by the paradoxes and inconsistencies highlighted, but felt more comfortable doing so through Korach’s mouth!)

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  • Cool. He is actually complaining about the precurser to my example, that פריחה works at all. I'll amend my post to mention that, but I was focused on the next step, that פריחה only works if it was tamei.
    – MichoelR
    Commented Jul 30, 2023 at 13:16

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